In my over six decades (well the last 5 of 'em) I have seen adds for many things, Super High Millage Carburetors and devices to make your car go farther on a gallon of gas.. Things that guarantee to cut your electric bill (And one of them actually does, Will discuss that), and more Magic this, Miracle That.
I have seen a demonstration (Video) of an engine that runs on all sorts of******(Waste oil, soda pop, water, basically any liquid) Amazing inventions.
I will start by explaining the engine... The poured the liquids into a standard water lock bottle, this is a bottle that has two pipes that extend down into it, one short, one long (the long one goes to near the bottom) the engine was hooked to the short pipe.. The man started it up, the liquids "Boiled" and the engine ran clean, as clean in fact as if it were powered by propane.
Attached to the long pipe (the one that extended down into the liquid) was a hose that ran out of sight.. I am 100% sure it was hooked to a propane tank.
So that's how he did it.
Why to I tell this... To explain how scammers scam.
I seriously doubt your Tesla device was, in fact, invented by Tesla. nor do I think it will improve your electric bill.
Oh, the one device that actually does? It is called a power factor controller.. Take devices that have motors (They only work on inductive loads) and plug one of these into its power line,, Could be a Furnace, Air conditioner (Very good here) De-Humidifier (what i used it on) Refrigerator, Any device with a motor.
They measure the Power factor (NOTE: if you wish I can explain how that works but if you want to measure a Power Factor,, the Kill-a-watt meter (About a kilo-buck worth of meters in a 20 dollar box) has a PF button,, Power factor)
The ideal power factor is 1.0,, This means that every watt is doing exactly 1 watt worth of work.
Some motors may be as low as 0.5, I have heard of cases where it hit 0.0. (Lots of power in, no energery out). the Power factor controllers try to bring the power factor up to 1.0
IF you see a label with "Volt-Amps" printed on it, That means Volts times Amps, this is what you pay for.. Volts Times Amps, Times POWER FACTOR, is what you get. So bringing the power factor closer to 1.0, means you use less power.